Problem: Rewrite as a simplified fraction. ${3.41\overline{5} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3415.5555...\\ 100x &= 341.5555...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3074}$ ${x = \dfrac{3074}{900}} $ ${x = \dfrac{1537}{450}} \text{or} {3 \dfrac{187}{450}}$